Preheat your oven to 350°F (175°C) and line two baking sheets with parchment paper.

In a large mixing bowl, cream together the softened unsalted butter, granulated sugar, and brown sugar until light and fluffy.

Incorporate the eggs one at a time and stir in the pure vanilla extract until smooth.

In a separate bowl, whisk together the gluten-free flour, baking powder, baking soda, salt, cinnamon, and optional nutmeg.

Gradually add the dry ingredients to the wet mixture, mixing just until incorporated.

Fold in the diced fresh peaches and old-fashioned oats into the cookie dough.

Drop mounds of dough onto the prepared baking sheets, leaving about 2 inches between each cookie.

Bake for 12-15 minutes, looking for golden edges and slightly soft centers.

Let the cookies cool on the baking sheets for about 5 minutes before transferring to a wire rack.